Our intention with this paper is to present ideas from the literature on functional data analysis and to show how to use them to model data from electricity markets. Electricity consumption during one day is an inherently smooth flow variable and this feature can be exploited to obtain more precise model estimates and better predictions. Each day of 24 hours is considered as one observation because of the diurnal seasonal pattern. Instead of considering the 24 hourly observations as a 24-dimensional vector they are considered as points on a curve. Two functional data techniques, functional analysis of variance (FANOVA) and a functional autoregressive (FAR) model, are used to do this with the purpose of data exploration and forecasting, respectively. The FANOVA analysis is useful for studying the seasonal patterns of consumption and the FAR analysis is shown to improve univariate forecasts.